A particle is acted on by two torques about the origin: t1 has magnitude of 2.0 Nm and is directed in the positive direction of the x axis. t2 has a magnitude of 4.0 Nm and is directed in the negative direction of the y axis (note the bold face of the torques indicates that they are vectors). Find dl/dt, where l is the angular momentum vector of the particle about the origin.

(hrw8c11p28) A particle P with mass 9 kg has position vector r (r = 6.0 m) and velocity v (v = 35.0 m/s) as shown in the figure. It is acted on by force F (F = 11.0 N). All three vectors lie in the xy plane. About the origin, what is the z-component of the angular momentum of the particle? About the origin, what is the z-component of the torque acting on the particle?

Two 4.80 kg balls are attached to the ends of a thin rod of length 40.0 cm and negligible mass. The rod is free to rotate in a vertical plane without friction about a horizontal axis through its center. With the rod initially horizontal (the figure), a 690 g wad of wet putty drops onto one of the balls, hitting it with a speed of 4.21 m/s and then sticking to it. (a) What is the angular speed of the system just after the putty wad hits? (b) What is the ratio of the kinetic energy of the system after the collision to that of the putty wad just before? (c) Through what angle (deg) will the system rotate before it momentarily stops? Putry wad Rotation axis (a) Number Units (b) Number Units (c) Number Units

At the instant of the figure, a 8.90 kg particle P has a position vector of magnitude 6.60 m and angle 01 = 42.0° and a velocity vector of magnitude 7.90 m/s and angle 02 = 31.0°. Force 7, of magnitude 8.70 N and angle 03 = 31.0° acts on P. All three vectors lie in the xy plane. About the origin, what are the magnitude of (a) the angular momentum of the particle and (b) the torque acting on the particle? (a) Number i (b) Number i V 0₂ Units Units F03/ -X ◄► ◄►

A particle P with mass 8 kg has position vector r (r = 3.0 m) and velocity v (v = 30.0 m/s) as shown in the figure. It is acted on by force F (F = 4.0 N). All three vectors lie in the xy plane. About the origin, what is the z-component of the angular momentum of the particle? About the origin, what is the z-component of the torque acting on the particle?

A bug is on the surface of a small wheel, which is a solid disk.

Two disks are initially spinning, one above the other on a small axle that provides a small, but non-negligible torque from friction, as shown in the figure below. Both disks have the same radius, R = 2.58 m. Disk 1 has a moment of inertia I1 = 9.8 kg⋅m2. Disk 2 has a moment of inertia I2 = 5 kg⋅ m2. Let vertically up be the z direction, such that counterclockwise rotation as viewed from above corresponds to positive values of the z-component. Disk 1 is initially spinning with a z-component of angular velocity ω1,z = 21 rad/s, and disk 2 is initially spinning with a z-component of angular velocity ω2,z = -15 rad/s. The z component of their common angular velcoity is 8.837 rad/s How much thermal energy is created in the process of disk 1 falling on disk 2 such that they reach a common final angular velocity? You do not need to worry about the gravitational potential energy because the initial separation of the disks is small. I get I need to use kinetic energy equations of 1/2*I*w2 but…

A solid spherical ball starts from rest at an initial height of 1.9 m, and rolls down an incline. The ball's mass is 2.5 kg and its radius is 23.2 cm. What is the ball's final center of mass (translational) speed (in m/s)?

A person of mass m = 75 kg stands in the center of a large rotating disk with radius R = 5.0 m and total mass M. The rotates without friction and without any external torque, initially at an angular velocity of w. The moment of inertia of a disk is MR. Assume that the person can be approximated as point-like, i.e. the angular momentum is r x p. The person then walks radially outward. (a) What is the angular momentum of the system (person + disk) as a function of the person's radius, r, from the center? Write it in terms of m, M, R, and w. (b) If the disk is initially rotating at wo and it slows to wp =0.8 rad/s when the person is at the very edge, what is the mass of the disk? 1.1 rad/s when the person is in the exact center, (c) What is the rotational kinetic energy of the system before and after the person walks to the edge?

A ring (mass 4 M, radius 1 R) rotates in a CCW direction with an initial angular speed 2 ω. A disk (mass 2 M, radius 2 R) rotates in a CW direction with initial angular speed 4 ω. The ring and disk "collide" and eventually rotate together. Assume that positive angular momentum and angular velocity values correspond to rotation in the CCW direction.What is the initial angular momentum Li of the ring+disk system? Write answer in terms of MR2ω.   What is the final angular velocity ωf of the ring+disk system? Write your answer in terms of ω.